The 27-year-old Bosnia-Herzegovina international, whose current deal runs out in the summer of 2016, has been quiet on his future plans while continually being linked with a move away from the Britannia.
Hughes, who recently tied down second-choice keeper Jack Butland to a new long-term contract, says he is delighted with Begovic and wants him to stay.
???The plan is to sit down with Asmir and his people at the end of the season and have an adult discussion and see where it takes us,??? he said ahead of his side???s penultimate Premier League game of the season at Burnley.
???My view hasn???t changed. I want him to stay here. I think we can offer him a good platform and are a good option for a lot of players, including him. He???s been outstanding in his time here and I want that to continue.
???We are conscious that he???s in the last year of his contract and we???ll discuss that situation with Asmir and his people.
“We???re not really into the detail yet. When we sit down then we???ll know what Asmir???s or his representatives??? aspirations are. Financial demands will always be part of the discussion, that???s a given, but I don???t think that???s something that we couldn???t overcome any discrepancy.
???Hopefully it will be resolved positively then.???
Begovic joined Stoke from Portsmouth for ??3.25million in the winter window of 2010 and has made 171 appearances for the club.